Whislt chatting to PCGamesN during E3, Stadia's head of communications Patrick Seybold said that Stadia users will be able to change their gamertags whenever they like, and as many times as they want.
If the username that you want is free, then you can grab it, like you would on Steam. Valve doesn't ask you to fork over cash for a different handle, whereas Xbox and PlayStation do charge you to change your tag. There's no word on whether or not Google will be looking for you to fork over a couple of bob to change your name, though. I'm sure, like a lot of other information on Stadia, that information will come in due course.
Prior to E3, Google did drop some Stadia-shaped details. It's scheduled to launch this November, with a library of 30 games. Those who want in on the ground floor can pre-order the Founder's Edition now, which includes a controller, a Chromecast Ultra, and two subscriptions to Stadia Pro. Have a read of this if you want to know more.